The Foxes have impressed since Frank Burrows took over as caretaker-manager last month, and they will feel that they should have recorded back-to-back wins for the first time since last April.
Following on from last weekend's victory over Barnsley, Leicester raced into an early lead thanks to a slick finish from striker Collins John.
The Fulham loanee had scored in the 2-0 win over the Tykes, and came up trumps again by sweeping home an excellent cross from fellow striker Dudley Campbell from close in after just seven minutes.
And the lively John nearly scored a second midway through the first half when he almost benefited from a collision between Colchester team-mates Dean Gerken and Matthew Connolly.
An empty goal beckoned, but defender Connolly recovered to block John's shot.
The home side grabbed the equaliser in the last minute of the first half. Mark Yeates again impressed down the right wing, and it was his precise cross that enabled Johnnie Jackson to head home at the near post, even though keeper Marton Fulop got his hands to the ball.
Chances were few and far between during the second period although it was Leicester who looked the more likely winners.
Bruno N'Gotty sliced a shot wide from a good position, while striker Matt Fryatt went close with a couple of fierce shots.
This was Colchester's first draw in their last seven matches, and they will perhaps be the happier of the two sides following two recent defeats on the road at Ipswich Town and Coventry City.
There was also the bonus of a first appearance of the season from key midfielder Kevin Watson, who had been sidelined with Achillies tendon and calf injuries.
Watson was the best player on the park before hobbling off with cramp just after the hour mark.